References
- Auslander , A. and Buchsbaum , D. 1958 . Codimension and multiplicity . Ann. Math , 68
- Bhattacharya , P.B. 1957 . The Hilbert function of two ideals . Proc. Cambridge Philos. Soc , 53 : 568 – 575 .
- Cuong , N.T. , Schenzel , P. and Trung , N.V. 1978 . Verallgemeinerte Cohen-Macaulay-Modun . Math. Nachr , 85 : 57 – 73 .
- Herzog , J. , Trung , N.V. and Ulrich , B. 1992 . On the multiplicity of blow-up rings of ideals generated by d-sequences . J. Pure Appl. Algebra , 80 : 273 – 297 .
- Herrmann , M. , Hyry , E. , Ribbe , J. and Tang , Z. 1997 . Reduction numbers and multiplicities of multigraded structures , 80 Preprint
- Katz , D. and Verma , J.K. 1989 . Extended Rees algebras and mixed multiplicities . Math. Z , 202 : 111 – 128 .
- Northcott , D.G. and Rees , D. 1954 . Reduction of ideals in local rings . Math. Proc. Cambridge Phil. Soc , 50 : 145 – 158 .
- Rees , D. 1961 . A-transforms of local rings and a theorem on multiplicities of ideals . Proc. Cambridge. Philos. Soc , 57 : 8 – 17 .
- Rees , D. 1981 . Hilbert functions and pseudo-rational local rings of dimension two . J. London Math. Soc , 24 : 467 – 479 .
- Rees , D. 1984 . Generalisations of reductions and mixed multiplicities . J. London Math. Soc , 29 : 397 – 414 .
- Swanson , I. 1992 . “ Tight Closure, Joint Reductions, and mixed multiplicities ” . In Thesis , Purdue University .
- Teissier , B. 1973 . “ Cycles èvanescents, sections planes, et conditions de Whitney ” . In Singularities à Cargése , Vol. 7-8 , 285 – 362 . Astérisque .
- Trung , N.V. 1987 . Reduction exponents and degree bound for thr defining equation of graded rings . Proc. Amer. Soc , 101 : 229 – 234 .
- Trung , N.V. 1993 . Filter-regular sequences and multiplicity of blow-up rings of ideals of the principal class . J. Math. Kyoto. Univ , 33 : 665 – 683 .
- Verma , J.K. 1988 . Rees algebras and mixed multiplicities . Proc. Am. Math. Soc , 104 : 1036 – 1044 .
- Verma , J.K. 1988 . Rees algebras with minimal multiplicity . Communications in Agebra , 17 ( 12 ) : 2999 – 3024 .
- Verma , J.K. 1988 . Multi-graded Rees algebras and mixed multiplicities . Proc. Amer. Math. Soc , 104 ( 12 ) : 1036 – 1044 .
- Verma , J.K. 1992 . Multi-graded Rees algebras and mixed multiplicities . J. Pure Appl. Algebra , 77 ( 12 ) : 219 – 228 .